The roles of the evolution of vortices on the aerodynamic noise of flapping wings

The effects of the evolution of vortices on the noise generated by a low-aspect-ratio flapping wing during hovering flight are investigated by solving the three-dimensional incompressible Navier-Stokes (N-S) equations. A simplified model based on the Ffowcs Williams-Hawkings (FW-H) acoustic analogy is developed here for investigating the aerodynamic noise of flapping wings, where the time derivative of the surface pressure is considered as the main contributor of far-field sound. A rigid rectangular wing with an aspect ratio of 1.5 undergoing both pitching and flapping motions at a Reynolds number (Re) of 1000 and a Mach number (M) of 0.04 is chosen for this study. By incorporating a Green's function, the time derivative of the surface pressure is found to be determined by the time derivatives of the divergence of the convection, the centrifugal acceleration and Coriolis acceleration terms in a non-inertial reference frame, with the first being the dominant source which is mainly within the vortical structure. Further, the Green's function is found to determine the time derivative of the surface pressure, which is related to the movement of the vortices. A scaling analysis is conducted on the time derivative of the surface pressure forces, revealing a scaling relationship with the cube of the flapping frequency f_o.